Abstract: This paper proposes methods to improve Monte Carlo estimates when the Independent Metropolis-Hastings Algorithm (IMHA) is used. Our first approach uses a control variate based on the sample generated by the proposal distribution. We derive the variance of our estimator for a fixed sample size and show that, as tends to infinity, this variance is asymptotically smaller than the one obtained with the IMHA. Our second approach is based on Jensen's inequality. We use a Rao-Blackwellization and exploit the lack of symmetry in the IMHA. An upper bound on the improvements that we can obtain by these methods is derived.
Key words and phrases: Control variates, Metropolis-hastings algorithm, Rao-Blackwellization, symmetry.